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Fractional Calculus of Fractal Interpolation Function on [0,b](b>0)

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  • XueZai Pan

Abstract

The paper researches the continuity of fractal interpolation function’s fractional order integral on [0,+∞) and judges whether fractional order integral of fractal interpolation function is still a fractal interpolation function on [0,b](b>0) or not. Relevant theorems of iterated function system and Riemann‐Liouville fractional order calculus are used to prove the above researched content. The conclusion indicates that fractional order integral of fractal interpolation function is a continuous function on [0,+∞) and fractional order integral of fractal interpolation is still a fractal interpolation function on the interval [0,b].

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Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:640628
DOI: 10.1155/2014/640628
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